A344225 a(n) = Sum_{k=1..n} tau(gcd(k,n)^(n/gcd(k,n))), where tau(n) is the number of divisors of n.

1, 3, 4, 8, 6, 17, 8, 23, 17, 35, 12, 57, 14, 61, 44, 74, 18, 123, 20, 121, 72, 137, 24, 215, 47, 187, 96, 217, 30, 387, 32, 261, 152, 311, 100, 488, 38, 385, 204, 441, 42, 813, 44, 505, 294, 557, 48, 961, 93, 739, 332, 697, 54, 1333, 188, 787, 408, 875, 60, 1723, 62, 997, 488, 976, 244, 2433, 68

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{d|n} phi(n/d) * tau(d^(n/d)).

If p is prime, a(p) = 1 + p.

Mathematica

Table[Sum[DivisorSigma[0, GCD[k, n]^(n/GCD[k, n])], {k, n}], {n, 100}] (* Giorgos Kalogeropoulos, May 13 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, numdiv(gcd(k, n)^(n/gcd(k, n))));
(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*numdiv(d^(n/d)));

Crossrefs

Cf. A344221, A344222, A344223, A344224.

Sequence in context: A330575 A079787 A081307 * A081543 A328876 A105753

Adjacent sequences: A344222 A344223 A344224 * A344226 A344227 A344228

Keyword

nonn

Author

Seiichi Manyama, May 12 2021

Status

approved